Finite Group Databasebeta

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C4×#15689194 #26214627

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#15689194

Splittings

FittingC22×C4×C8×C47 ⋊ C2
SylowC47 ⋊ C4×#435

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC22×C4×C8×C47C2
socleC23×C47C23×C4
prime radicalC22×C22⋊D47C2×C4
cosocleC22×C4×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C4×#435
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C22×C4×C8

1282 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167917);